non thermal cp violation in soft leptogenesis€¦ · and neutrons) in the universe in unequal to...

Evidence of Matter Anti-Matter AsymmetryTypes of Baryogenesis

LeptogenesisConclusion

Non thermal CP violation in Soft Leptogenesis

Arnab Dasgupta

Institute of Physics, BhubaneshwarCollaborators:

Raghavan Rangarajan, Chee Fong Sheng andRathin Adhikari

Humbolt UniversityJuly 2, 2015

Arnab Dasgupta Non thermal CP violation in Soft Leptogenesis



1 Evidence of Matter Anti-Matter Asymmetry

2 Types of BaryogenesisGrand Unified Theory (GUT) baryogenesisElectroweak BarogenesisAffleck-Dine MechanismLeptogenesis

3 LeptogenesisBasic LeptogenesisSoft LeptogenesisPhenomenological Constraints

4 Conclusion




Observations indicate that the number of baryons (protonsand neutrons) in the Universe in unequal to the numbers ofanti-baryons (anti protons and anti- neutrons).

There are many evidences for believing in suchasymmetry.

1 The very fact we exist on earth gives us a convincingevidence that anti-matter is rare on earth.

2 At larger scales, if matter galaxies and anti-matter galaxiesexisted at same cluster then there would be huge amountof γ-ray emission from nucleon-anti nucleon annihilations.

The observed baryon asymmetry must have beengenerated dynamically, a scenario that is known by thename of Baryogenesis.




Observations indicate that the number of baryons (protonsand neutrons) in the Universe in unequal to the numbers ofanti-baryons (anti protons and anti- neutrons).There are many evidences for believing in suchasymmetry.

1 The very fact we exist on earth gives us a convincingevidence that anti-matter is rare on earth.

2 At larger scales, if matter galaxies and anti-matter galaxiesexisted at same cluster then there would be huge amountof γ-ray emission from nucleon-anti nucleon annihilations.

The observed baryon asymmetry must have beengenerated dynamically, a scenario that is known by thename of Baryogenesis.




The baryon asymmetry of the Universe can be defined in thefollowing way.

Y∆B =nB − nB

s

∣∣∣∣0

= (6.21± 0.16)× 10−10




There are three ingredient to generate baryon asymmetrywhich were given by Sarkhov

1 Baryon number violation2 C and CP violation3 Out of Equilibrium dynamics

All of the above ingredients are there in Standard Model.But still it does not generates enough asymmetry.





1 Baryon number violation

2 C and CP violation3 Out of Equilibrium dynamics






1 Baryon number violation2 C and CP violation

3 Out of Equilibrium dynamics






1 Baryon number violation2 C and CP violation3 Out of Equilibrium dynamics





The Baryogenesis requires new physics that extends theStandard Model in at least two ways:

1 It must introduce new source of CP violation.2 It must either provide a departure from thermal equilibrium

in addition to the electroweak phase transition (EWPT) ormodify the EWPT itself.





1 It must introduce new source of CP violation.

2 It must either provide a departure from thermal equilibriumin addition to the electroweak phase transition (EWPT) ormodify the EWPT itself.





1 It must introduce new source of CP violation.2 It must either provide a departure from thermal equilibrium

in addition to the electroweak phase transition (EWPT) ormodify the EWPT itself.




Grand Unified Theory (GUT) baryogenesisElectroweak BarogenesisAffleck-Dine MechanismLeptogenesis

Some new physics mechanisms for baryogenesis are asfollows:

1 Grand Unified Theory (GUT) baryogenesis2 Electroweak baryogenesis3 Affleck-Dine mechanism4 Leptogenesis






1 Grand Unified Theory (GUT) baryogenesis

2 Electroweak baryogenesis3 Affleck-Dine mechanism4 Leptogenesis






1 Grand Unified Theory (GUT) baryogenesis2 Electroweak baryogenesis

3 Affleck-Dine mechanism4 Leptogenesis






1 Grand Unified Theory (GUT) baryogenesis2 Electroweak baryogenesis3 Affleck-Dine mechanism

4 Leptogenesis






1 Grand Unified Theory (GUT) baryogenesis2 Electroweak baryogenesis3 Affleck-Dine mechanism4 Leptogenesis





It generates the baryon asymmetry in the out-of-equilibriumdecays of heavy bosons in GUT. The GUT baryogenesis hasdifficulties with the non-observation of proton decay, which putsa lower bound on the mass of the decaying boson, andtherefore on the reheat temperature after inflation.





Its a class of models where the departure from thermalequilibrium is provided by the electroweak phase transitions. Inprinciple, Standard Model belongs to this class, but the phasetransition is not strongly first order and the CP violation is toosmall. Thus, viable models of electroweak baryogenesis need amodification of the scalar potential such that the nature of theEWPT changes, and new sources of CP violation.





The asymmetry arises in classical scalar field, which laterdecays to particles. In a SUSY model, this field could be somecombination of squark, Higgs and slepton field. This field startsfrom a large expectation value then starts to roll down to theorigin. While starting from large initial value and rolling down toorigin, there can be contribution from baryons and leptonsviolating interactions. These impart a net asymmetry from therolling field.





After the discovery of neutrino oscillation, Leptogenesisgained much attention as one can explain the neutrinomass with matter anti-matter asymmetry in one singleframework.

It was first proposed by Fukugita and Yanagida 1. Newparticles-singlet neutrinos- are introduced via the see sawmechanism. Their couplings provide the necessary newsource of CP violation. The rate of these Yukawainteractions can be slow enough that departure fromthermal equilibrium occurs. Lepton number violationcomes from the Majorana masses of these new particles.

1M. Fukugita and T. Yanagida. “Baryogenesis Without Grand Unification”.In: Phys.Lett. B174 (1986), p. 45. DOI: 10.1016/0370-2693(86)91126-3


http://dx.doi.org/10.1016/0370-2693(86)91126-3




After the discovery of neutrino oscillation, Leptogenesisgained much attention as one can explain the neutrinomass with matter anti-matter asymmetry in one singleframework.It was first proposed by Fukugita and Yanagida 1. Newparticles-singlet neutrinos- are introduced via the see sawmechanism. Their couplings provide the necessary newsource of CP violation. The rate of these Yukawainteractions can be slow enough that departure fromthermal equilibrium occurs. Lepton number violationcomes from the Majorana masses of these new particles.

1M. Fukugita and T. Yanagida. “Baryogenesis Without Grand Unification”.In: Phys.Lett. B174 (1986), p. 45. DOI: 10.1016/0370-2693(86)91126-3


http://dx.doi.org/10.1016/0370-2693(86)91126-3



Basic LeptogenesisSoft LeptogenesisPhenomenological Constraints

Generation of Lepton asymmetry

Generate Leptonasymmetry

φ φ†

l l

N N N

Washout of leptonasymmetry

φ φ†

l lN N N

T = MN

Temperature of the Universe drops below e−MN/T due tothe expansionSuppresion of the inverse decay by a factorLepton asymmetry is generated !!







φ φ†

l l

N N N


φ φ†

l lN N N

T = MN

Temperature of the Universe drops below e−MN/T due tothe expansion

Suppresion of the inverse decay by a factorLepton asymmetry is generated !!







φ φ†

l l

N N N


φ φ†

l lN N N

T = MN

Temperature of the Universe drops below e−MN/T due tothe expansionSuppresion of the inverse decay by a factor

Lepton asymmetry is generated !!







φ φ†

l l

N N N


φ φ†

l lN N N

T = MN

Temperature of the Universe drops below e−MN/T due tothe expansionSuppresion of the inverse decay by a factorLepton asymmetry is generated !!





Conversion of the Lepton asymmetry to the baryonasymmetry

Violation of B + L due to the non-trivial structure ofnon-abelian gauge theories, while B - L is conserved.Transitions from one vacuum structure to another with achange of B and L by 3 units.Energy barrier between two vacuum structures which isovercome through thermal excitations - spheleron






Violation of B + L due to the non-trivial structure ofnon-abelian gauge theories, while B - L is conserved.

Transitions from one vacuum structure to another with achange of B and L by 3 units.Energy barrier between two vacuum structures which isovercome through thermal excitations - spheleron






Violation of B + L due to the non-trivial structure ofnon-abelian gauge theories, while B - L is conserved.Transitions from one vacuum structure to another with achange of B and L by 3 units.

Energy barrier between two vacuum structures which isovercome through thermal excitations - spheleron






Violation of B + L due to the non-trivial structure ofnon-abelian gauge theories, while B - L is conserved.Transitions from one vacuum structure to another with achange of B and L by 3 units.Energy barrier between two vacuum structures which isovercome through thermal excitations - spheleron





Boltzmann Equations

dηNαdz

= −(ηNαηNeq− 1

)(Dα + Sα),

dη∆Ll

dz=∑

α

εlα

(ηNαηNeq− 1

)Dα −

2

3η∆Ll Wl

ηNα = nNα /ηγ , η∆L = n∆Ll /nγ , z = MN/T,HN = H(z = 1)

Dα =z

ηγHN

∑

k

γDkα, Dα =z

ηγHN

∑

k

γDkα, Sα =z

ηγHN

∑

k

γSkα,

Wl =z

ηγHN

[∑

α

(Blα

∑

k

γDkα + γSlα

)+∑

k

(γ

(∆L=2)lk + γ

(∆L=0)lk

)]





This mechanism have

1 A Lepton violating interaction (∆L 6= 0) (Baryon numberviolation)

2 Which in general gives new CP violating phases in theneutrino Yukawa intractions (C and CP violation)

3 And for large part of the parameter space predicts that new,heavey singlet neutrinos decay out of equilibrium (Out ofEquilibrium dynamics)

CHECK LIST COMPLETE !!





This mechanism have1 A Lepton violating interaction (∆L 6= 0) (Baryon number

violation)

2 Which in general gives new CP violating phases in theneutrino Yukawa intractions (C and CP violation)








violation)2 Which in general gives new CP violating phases in the

neutrino Yukawa intractions (C and CP violation)








violation)2 Which in general gives new CP violating phases in the

neutrino Yukawa intractions (C and CP violation)3 And for large part of the parameter space predicts that new,

heavey singlet neutrinos decay out of equilibrium (Out ofEquilibrium dynamics)






But a potential drawback of leptogenesis is the lowerbound on MN (mass of heavy Right handed neutrino),which gives a lower bound on reheat temperature which isTreh > 109 GeV.

This bound might be in conflict with an upper bound on thereheat that applies in supersymmetric models with a”gravitino problem”.After inflation, the universe thermalizes to a reheattemperature Treheat. Gravitinos are produced by thermalscattering in that bath, and the rate is higher at highertemperatures. The gravitinos are long-lived; if there arelighter SUSY particles (the gravitino is not the LSP), thedecay rate can be estimated to be

Γ ∼m3grav

m2pl

'(mgrav

20TeV

)3

s−1





But a potential drawback of leptogenesis is the lowerbound on MN (mass of heavy Right handed neutrino),which gives a lower bound on reheat temperature which isTreh > 109 GeV.This bound might be in conflict with an upper bound on thereheat that applies in supersymmetric models with a”gravitino problem”.

After inflation, the universe thermalizes to a reheattemperature Treheat. Gravitinos are produced by thermalscattering in that bath, and the rate is higher at highertemperatures. The gravitinos are long-lived; if there arelighter SUSY particles (the gravitino is not the LSP), thedecay rate can be estimated to be

Γ ∼m3grav

m2pl

'(mgrav

20TeV

)3

s−1





But a potential drawback of leptogenesis is the lowerbound on MN (mass of heavy Right handed neutrino),which gives a lower bound on reheat temperature which isTreh > 109 GeV.This bound might be in conflict with an upper bound on thereheat that applies in supersymmetric models with a”gravitino problem”.After inflation, the universe thermalizes to a reheattemperature Treheat. Gravitinos are produced by thermalscattering in that bath, and the rate is higher at highertemperatures. The gravitinos are long-lived; if there arelighter SUSY particles (the gravitino is not the LSP), thedecay rate can be estimated to be

Γ ∼m3grav

m2pl

'(mgrav

20TeV

)3

s−1





If too many gravitinos decay during or after Big BangNucleosynthesis (t ∼ s), the resulting energetic showers inthe thermal bath destroy the agreement between predictedand observed light element abundances.

One of the plausible solution is to have small reheatingtemperature Treh < 106 − 1010 GeV so that the gravitinodensity is small. Which is provided by ”Soft Leptogenesis”.





If too many gravitinos decay during or after Big BangNucleosynthesis (t ∼ s), the resulting energetic showers inthe thermal bath destroy the agreement between predictedand observed light element abundances.One of the plausible solution is to have small reheatingtemperature Treh < 106 − 1010 GeV so that the gravitinodensity is small. Which is provided by ”Soft Leptogenesis”.





In the framework of supersymmetric see saw models, newleptogenesis mechanism become plausible, Softleptogenesis.

This is a new mechanism which does not require flavourmixing among the right handed neutrinos.In the framework of the supersymmetric standard modelextended to include singlet neutrinos (SSM+N), there are,in addition to the soft supersymmetry breaking terms of theSSM, terms that involve the singlet sneutrinos N , inparticular biliniear (B) and the trilinear (A) scalar couplings.





In the framework of supersymmetric see saw models, newleptogenesis mechanism become plausible, Softleptogenesis.This is a new mechanism which does not require flavourmixing among the right handed neutrinos.

In the framework of the supersymmetric standard modelextended to include singlet neutrinos (SSM+N), there are,in addition to the soft supersymmetry breaking terms of theSSM, terms that involve the singlet sneutrinos N , inparticular biliniear (B) and the trilinear (A) scalar couplings.





In the framework of supersymmetric see saw models, newleptogenesis mechanism become plausible, Softleptogenesis.This is a new mechanism which does not require flavourmixing among the right handed neutrinos.In the framework of the supersymmetric standard modelextended to include singlet neutrinos (SSM+N), there are,in addition to the soft supersymmetry breaking terms of theSSM, terms that involve the singlet sneutrinos N , inparticular biliniear (B) and the trilinear (A) scalar couplings.





Soft breaking terms gives a small mass splitting betweenthe CP-even and CP-odd right-handed sneutrinos states ofa single generation and provide a CP-violating phasesufficient to generate a lepton asymmetry.

Contrary to leptogenesis from neutrino decay, a singlegeneration right-handed sneutrino decay is sufficient togenerate the CP asymmetry.

The supersymmetric see-saw model is described by thesuperpotential

W = YijNiLjH +1

2MijNiNj

The supersymmetry-breaking terms involving the right handedsneutrino Ni are

−Lsoft = m2ijN

†i Nj +

(AijYijNi ljH +

1

2BijMijNiNj + h.c

)





Soft breaking terms gives a small mass splitting betweenthe CP-even and CP-odd right-handed sneutrinos states ofa single generation and provide a CP-violating phasesufficient to generate a lepton asymmetry.Contrary to leptogenesis from neutrino decay, a singlegeneration right-handed sneutrino decay is sufficient togenerate the CP asymmetry.

The supersymmetric see-saw model is described by thesuperpotential

W = YijNiLjH +1

2MijNiNj

The supersymmetry-breaking terms involving the right handedsneutrino Ni are

−Lsoft = m2ijN

†i Nj +

(AijYijNi ljH +

1

2BijMijNiNj + h.c

)





The right handed neutrino N has mass, while sneutrino andanti-sneutrino states mix in the mass matrix. Their masseiganvectors

N+ =1√2

(eiφ/2N + e−iφ/2N †

), N− = − i√

2

(eiφ/2N − e−iφ/2N †

)

with φ = arg[BM ], have mass eigenstate

M2± = M2 + M2 ± |BM |





The sneutrino interaction Lagrangian in the basis of flavour(N , N †) and the mass (N+, N−) eigenstate is respectively

−Lint = N(Y1iHl

iL +mY ∗1i l

∗iH∗ +AY1i liH

)+ h.c

=Y1i√

2N+

(HliL + (A+M)liH

)+ i

Y1i√2

[HliL + (A−M)liH

]





The CP asymmetry is given as

ε =4ΓB

4B2 + Γ2

Im(A)

M∆BF ; ∆BF =

cB − cFcB + cF

where the resonance happens for Γ ∼ 2B or else there is anextra suppression.

The thermal parts cB and cF are due to the bose stimulationand pauli blocking respectively.But the interesting part is that the diagrams which areconsidered while doing these calculation do not consider onecondition due to which they missed out the non-thermal part...!!






ε =4ΓB

4B2 + Γ2

Im(A)

M∆BF ; ∆BF =

cB − cFcB + cF

where the resonance happens for Γ ∼ 2B or else there is anextra suppression.The thermal parts cB and cF are due to the bose stimulationand pauli blocking respectively.

But the interesting part is that the diagrams which areconsidered while doing these calculation do not consider onecondition due to which they missed out the non-thermal part...!!






ε =4ΓB

4B2 + Γ2

Im(A)

M∆BF ; ∆BF =

cB − cFcB + cF

where the resonance happens for Γ ∼ 2B or else there is anextra suppression.The thermal parts cB and cF are due to the bose stimulationand pauli blocking respectively.But the interesting part is that the diagrams which areconsidered while doing these calculation do not consider onecondition due to which they missed out the non-thermal part...!!





∑

fBF

|out〈f |X〉|2 −∑

fBF

|out〈f |X〉|2

=∑

fBF

∑

g 6=BF

[A∗(X → g)A(f → g)A∗(f → X)

− A∗(X → f)A(g → f)A∗(X → g)]

For 2-body decay scenario, the difference term, i.e, the term onthe right-hand side is 0 to O(λ2), where λ is any coupling in thetheory.





At O(λ4), the difference term can be written as

∑

fBF

∑

g 6=BF

[A∗c(X → g)Ac(f → g)A∗c(f → X)

−A∗c(X → f)Ac(g → f)A∗c(X → g)]

= 2Re∑

fBF

∑

gB 6=BF

[Ac(X → g)Ac(g → f)A∗c(X → f)]

The requirement for an asymmetry is that there must existdiagrams such that the process to the right of the ”cut” shouldviolate baryon number and the net asymmetry is thenproportional to the amplitude associated with these diagrams.





At O(λ4), the difference term can be written as∑

fBF

∑

g 6=BF

[A∗c(X → g)Ac(f → g)A∗c(f → X)

−A∗c(X → f)Ac(g → f)A∗c(X → g)]

= 2Re∑

fBF

∑

gB 6=BF

[Ac(X → g)Ac(g → f)A∗c(X → f)]

The requirement for an asymmetry is that there must existdiagrams such that the process to the right of the ”cut” shouldviolate baryon number and the net asymmetry is thenproportional to the amplitude associated with these diagrams.





CP violation

To quantify the CP violation, we define the CP asymmetry forthe decays N± → aα with aα = {˜αHu, `αHu} as

εS,V±α ≡γ(N± → aα)− γ(N± → aα)

∑aβ ;β

[γ(N± → aβ) + γ(N± → aβ)

] , (1)

where the superscripts S and V indicate the CP violationcoming from Self-energy (S) and Vertex (V ) correctionsrespectively





We showed that the diagrams which can be achieved whileincorporating the above condition in the context of Softleptogenesis are

N∓N±

ℓα

Hu

ℓβ

Hu

(c)

(f)

N∓N±

ℓα

Hu

ℓβ

Hu

N∓N±

ℓα

Hu

ℓβ

Hu

(b)

(e)

N∓N±

ℓα

Hu

ℓβ

Hu

N∓N±

ℓα

Hu

ℓβ

Hu

(a)

(d)

N∓N±

ℓα

Hu

ℓβ

Hu





εS,(a)±α =

1

4πG±(T )Y

2α

∑β

YβIm(Aβ)

M

(1 +

M2

M2±B

M

)2BM

4B2 + Γ2∓rB(T )cF (T ),

εS,(b)±α = −

1

4πG±(T )Y

2Yα

Im(Aα)

M

(1 +

M2

M2±B

M

)2BM

4B2 + Γ2∓rF (T )cB(T ),

εS,(c)±α =

1

4πG±(T )

Y 2 −∑β

|Aβ |2

M2

Yα Im(Aα)

M−(Y

2α −

|Aα|2

M2

)∑β

YβIm(Aβ)

M

×

2BM

4B2 + Γ2∓rB(T )cB(T ),

where we define Y 2 ≡∑α

Y2α and

G±(T ) ≡[Y

2+∑α

(|Aα|2

M2±

2YαRe(Aα)

M

)]cB(T ) + Y

2

(1 +

M2

M2±B

M

)cF (T ). (2)

In the above rB,F (T ) and cB,F (T ) are temperature dependent terms associated with intermediate on-shell and

final states respectively





If we sum over the lepton flavor α and use rF (T )cB(T ) = rB(T )cF (T ),we obtain

∑

α

(εS,(a)±α + ε

S,(b)±α

)=∑

α

εS,(c)±α = 0 in agreement with the

T = 0 result of Adhikari et. al.3








The total CP asymmetry from mixing εS±α ≡∑

n={a,b,c,d,e,f}εS,(n)±α is given by

εS±α =

1

4πG±(T )Y

2α

∑β

YβIm(Aβ)

M

4BM

4B2 + Γ2∓

[cF (T )− cB(T )] rB(T )

+1

4πG±(T )

|Aα|2

M2

∑β

YβIm(Aβ)

M

4BM

4B2 + Γ2∓rB(T )cB(T )

+1

4πG±(T )Y

2α

∑β

YβIm(Aβ)

M

(M2

M2±B

M

)4BM

4B2 + Γ2∓rB(T )cF (T ).

In the above, the first term vanishes in the zero temperature limit T → 0 when cB,F (T )→ 1 and

rB,F (T )→ 1 while the terms higher order in mSUSY/M survive





Thermal limit

In the limit Yα � Aα/M , we have

εS±α ' 1

4πPα∑

β

YβIm(Aβ)

M

4BM

4B2 + Γ2Y

cF (T )− cB(T )

cF (T ) + cB(T )rB(T ),

where we define the flavor projector Pα ≡ Y 2α /Y

2 with∑

α

Pα = 1 and

ΓY ≡Y 2M

4πand we have dropped the terms higher order in

mSUSY/M . In this case, the CP asymmetry in the above equation isproportional to cF (T )− cB(T ) which goes to zero as T → 0 andhence the contribution to the CP violation is the thermal one.





Non-Thermal limit

In the other limit Yα � Aα/M , we have

εS±α ' 1

4π

|Aα|2∑δ |Aδ|2

∑

β

YβIm(Aβ)

M

4BM

4B2 + Γ2A

rB(T ),

where ΓA ≡∑

α

|Aα|28πM

. The CP asymmetries in the above equation

clearly do not vanish at T = 0 and this represents a nonthermal CPviolation. Of course thermal effects are always there but the fact thatthe CP violation is nonvanishing at T = 0 implies that it is lesssuppressed compared to the case thermal case.





0.2 0.5 1.0 2.0 5.0 10.0K

1 ´ 10-112 ´ 10-11

5 ´ 10-111 ´ 10-102 ´ 10-10

5 ´ 10-101 ´ 10-92 ´ 10-9

ÈYD BH¥L ÈB=1 TeV, argH AΑL=-Π� 2, tanΒ=10

0.2 0.5 1.0 2.0 5.0 10.0K

1 ´ 10-112 ´ 10-11

5 ´ 10-111 ´ 10-102 ´ 10-10

5 ´ 10-101 ´ 10-92 ´ 10-9

ÈYD BH¥L ÈB=1 TeV, argH AΑL=-Π� 2, tanΒ=10

In the above plot

Non Thermal Dominated (blue dashed) : In this scenario we chooseA/M = (10−4, 10−2, 1)w and Y = (10−5, 10−3, 10−1)w.

Thermal Dominated (red dashed) : In this scenario we chooseA/M = (10−5, 10−3, 10−1)w and Y = (10−4, 10−2, 1)w.

Mixed (purple solid) : In this scenario we chooseA/M = (10−4, 10−2, 1)w and Y = (10−4, 10−2, 1)w.





From the above numerical exercise we can conclude two things

That the generation of sufficient baryon asymmetry ispossible for TeV scale Aα and B � Γ± i.e far away fromresonant regimeWe also see that nonthermal CP violation can significantlyenhance the efficiency of soft leptogenesis.





From the above numerical exercise we can conclude two thingsThat the generation of sufficient baryon asymmetry ispossible for TeV scale Aα and B � Γ± i.e far away fromresonant regime

We also see that nonthermal CP violation can significantlyenhance the efficiency of soft leptogenesis.





From the above numerical exercise we can conclude two thingsThat the generation of sufficient baryon asymmetry ispossible for TeV scale Aα and B � Γ± i.e far away fromresonant regimeWe also see that nonthermal CP violation can significantlyenhance the efficiency of soft leptogenesis.





Hu

ℓβ

N∓

ℓα

Hu

N±

(c)

Hu

N

ℓα

Hu

N±Hu

ℓβ

N

ℓα

Hu

N±

(a) (b)

ℓβ





εV±α = ∓

ln 2

8πG±(T )

Y 2Yα

Im(Aα)

M+ Y

2α

∑β

YβIm(Aβ)

M

[cF (T )− cB(T )] rB(T )

−1

8πG±(T )

Y 2Yα

Im(Aα)

M+ Y

2α

∑β

YβIm(Aβ)

M

B

M

[cF (T )

2+ (ln 2− 1)cB(T )

]rB(T )

∓ln 2

8πG±(T )

∑β

|Aβ |2

M2Yα

Im(Aα)

M+|Aα|2

M2

∑β

YβIm(Aβ)

M

rB(T )cB(T )

+1

8πG±(T )

∑β

|Aβ |2

M2Yα

Im(Aα)

M+|Aα|2

M2

∑β

YβIm(Aβ)

M

B

M(ln 2− 1)rB(T )cB(T ).





We are primarily interested in the mass range M > 107 GeV.

But even in M± ∼ TeV, the bound on the Yukawa couplingsfrom the requirement of out-of-equilibrium decays of N±

Γ± . H(T = M)√√√√[∑

α

Y 2α +|Aα|22M2

± YαReAαM

]. 1.6× 10−5

(M

107GeV

)1/2

which make N± impossible to be produced at colliders.





We are primarily interested in the mass range M > 107 GeV.But even in M± ∼ TeV, the bound on the Yukawa couplingsfrom the requirement of out-of-equilibrium decays of N±

Γ± . H(T = M)√√√√[∑

α

Y 2α +|Aα|22M2

± YαReAαM

]. 1.6× 10−5

(M

107GeV

)1/2

which make N± impossible to be produced at colliders.





For µ and τ EDM, me can be replaced by mµ and mτ but thecurrent experimental bounds on them are a lot weaker

|dµ|exp < 1.9× 10−19e− cm

|dτ |exp < 5.1× 10−17e− cm





Charged Lepton Flavor Violation

The branching ratio due to non-vanishing off diagonal elementsof the soft mass matrix of doublet slpeton m2

l

BR(lα → lβγ) ≈ α3

G2F

|(m2l)αβ|

m8SUSY

tan2 β

(m2l)αβ ≈ −

1

8π2A∗αAβ ln

(MGUT

M

)

for α 6= β





The MEG experiment gives most stringent bound

BR(µ→ eγ)exp < 5.7× 10−13

|A∗µAe| . 5× 103GeV2(mSUSY

1TeV

)4(

10

tanβ

)

where MGUT = 106 GeV and M = 107 GeV.

Similarly using the experimental bounds on τ decaysBR(τ → eγ)exp < 3.3× 10−18 and BR(τ → µγ)exp < 4.4× 10−8

|A∗τAe| ≈ |A∗τAµ| . 1× 106GeV2(mSUSY

1TeV

)4(

10

tanβ

)





The MEG experiment gives most stringent bound

BR(µ→ eγ)exp < 5.7× 10−13

|A∗µAe| . 5× 103GeV2(mSUSY

1TeV

)4(

10

tanβ

)

where MGUT = 106 GeV and M = 107 GeV.Similarly using the experimental bounds on τ decaysBR(τ → eγ)exp < 3.3× 10−18 and BR(τ → µγ)exp < 4.4× 10−8

|A∗τAe| ≈ |A∗τAµ| . 1× 106GeV2(mSUSY

1TeV

)4(

10

tanβ

)




Soft Leptogenesis is an interesting scenario in the framework ofthe supersymmetric seesaw for several reasons

1 The relevant new sources of CP violation and leptonnumber violation appear generically in this framework. Inthis sense, soft leptogenesis is qualitatively unavoidable inSSM+N framework, and the question of its relevance is aquantitative one.

2 If M < 109 GeV (in the supersymmetric framework, thisrange is preferred by the gravitino problem), then standardleptogenesis encounters problems, while softleptogenesiscan be significant.




Now after considering the ∆L 6= 0 to the right of the ”cut”, weshowed that with generic soft trilinear A couplings there are twointeresting consequences

3 One can realize non thermal CP violation where the CPasymmetries in the decays of heavy sneutrinos to leptonand sleptons do not cancel at zero temperature resulting inan enhanced efficiency in generating baryon asymmetry.

4 The dominant CP violation from self-energy corrections issufficent even far away from the resonant regime and therelevent soft parameters can assume natural values ataround the TeV scale.




THANK YOU!


non thermal cp violation in soft leptogenesis€¦ · and neutrons) in the universe in unequal to...

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